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If α and β are roots of the equation 3x2 – 13x + 14 = 0, what is the value of (α/β) + (β/α)?
- A65/28
- B53/14
- C9
- D85/42
Answer not set
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0
CCommunity
It can be written as (α2 + β2)/(αβ)
⇒ {(α + β)2 - 2αβ}/{αβ}
And from the quadratic equation αβ = 14/3 and α + β = 13/3, Putting this in the required
equation
⇒ {(13/3)2 – 2(14/3)}/{14/3}
⇒ {(169/3) - 28}/{14}
⇒ 85/42
∴ the value of (α/β) + (β/α) is 85/42
⇒ {(α + β)2 - 2αβ}/{αβ}
And from the quadratic equation αβ = 14/3 and α + β = 13/3, Putting this in the required
equation
⇒ {(13/3)2 – 2(14/3)}/{14/3}
⇒ {(169/3) - 28}/{14}
⇒ 85/42
∴ the value of (α/β) + (β/α) is 85/42
0
CCommunity
It can be written as (α2 + β2)/(αβ)
⇒ {(α + β)2 - 2αβ}/{αβ}
And from the quadratic equation αβ = 14/3 and α + β = 13/3, Putting this in the required
equation
⇒ {(13/3)2 – 2(14/3)}/{14/3}
⇒ {(169/3) - 28}/{14}
⇒ 85/42
∴ the value of (α/β) + (β/α) is 85/42
⇒ {(α + β)2 - 2αβ}/{αβ}
And from the quadratic equation αβ = 14/3 and α + β = 13/3, Putting this in the required
equation
⇒ {(13/3)2 – 2(14/3)}/{14/3}
⇒ {(169/3) - 28}/{14}
⇒ 85/42
∴ the value of (α/β) + (β/α) is 85/42